Finite Group Databasebeta

← #10733772

Subgroups — #10733772

Order 768.

2258 conjugacy classes of subgroups.

The subgroup lattice has 1210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×#5231C211yesmaximal, characteristic, complemented
3C2×#5213C211yesmaximal, characteristic
4C2×#4989C211yesmaximal, characteristic, complemented
5C2×#4987C211yesmaximal, characteristic, complemented
6C2×#4956C211yesmaximal, characteristic
7#72134C211yesmaximal, characteristic, complemented
8#72127C211yesmaximal, characteristic, complemented
9#71570C211yesmaximal, characteristic, complemented
10#71569C211yesmaximal, characteristic, complemented
11#71566C211yesmaximal, characteristic, complemented
12#71565C211yesmaximal, characteristic, complemented
13#71550C211yesmaximal, characteristic
14#71547C211yesmaximal, characteristic, complemented
15#71546C211yesmaximal, characteristic, complemented
16#15323—31nomaximal, Sylow
17C23×C3×Q8C2211yescharacteristic
18C24×C3×C4C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×C4×D3C2211yescharacteristic
21C2×C3×C22⋊Q8—24no—
22C2×C3×C22⋊Q8—24no—
23C2×C3×C22⋊Q8—24no—
24C22×C3×C4⋊C4C2211yescharacteristic
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×#217C2211yescharacteristic
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×C4⋊Dic3C2211yescharacteristic
38C22×Dic3⋊C4C2211yescharacteristic
39#5231—24no—
40#5213—24no—
41C2×C3⋊#95C2211yescharacteristic
42C2×C3⋊#95C2211yescharacteristic
43C2×C3⋊#95C2211yescharacteristic
44C2×C3⋊#95C2211yescharacteristic
45C2×C3⋊#95C2211yescharacteristic
46C2×C3⋊#95C2211yescharacteristic
47C2×C3⋊#95C2211yescharacteristic
48C2×C3⋊#95C2211yescharacteristic
49C2×C3⋊#95C2211yescharacteristic
50C2×C3⋊#95C2211yescharacteristic
51C2×C3⋊#95C2211yescharacteristic
52C2×C3⋊#95C2211yescharacteristic
53C2×C3⋊#95C2211yescharacteristic
54C2×C3⋊#95C2211yescharacteristic
55C2×C3⋊#95C2211yescharacteristic
56C2×C3⋊#95C2211yescharacteristic
57#4989—24no—
58#4987—24no—
59#4956—24no—
60C22×C22⋊Q8D311yescharacteristic, complemented
61C2×#393—31no—
62C2×#386—31no—
63C2×#386—31no—
64C2×#385—31no—
65C2×#380—31no—
66#1446—31no—
67#1445—31no—
68#1441—31no—
69#1441—31no—
70#1439—31no—
71#1439—31no—
72#1439—31no—
73#1438—31no—
74C22⋊#95—31no—
75C25×C3C2311yescharacteristic
76C24×D3C2311yescharacteristic
77C22×C3×Q8—22no—
78C22×C3×Q8—22no—
79C22×C3×Q8—22no—
80C22×C3×Q8—22no—
81C22×C3×Q8—22no—
82C22×C3×Q8—41no—
83C22×C3×Q8—41no—
84C23×C3×C4—22no—
85C23×C3×C4—22no—
86C23×C3×C4—22no—
87C23×C3×C4—22no—
88C23×C3×C4—22no—
89C23×C3×C4—41no—
90C23×C3×C4—41no—
91C23×C3×C4C2311yescharacteristic
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C22×#67—22no—
98C22×#67—22no—
99C22×#67—22no—
100C22×#67—22no—
101C22×#67—41no—
102C22×#67—41no—
103C22×#67Q814yescomplemented
104C23×Dic3C2311yescharacteristic
105C23×Dic3C2311yescharacteristic
106C23×Dic3C2311yescharacteristic
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C22×C4×D3—22no—
112C22×C4×D3—22no—
113C22×C4×D3—22no—
114C22×C4×D3—22no—
115C22×C4×D3—22no—
116C22×C4×D3—41no—
117C22×C4×D3—41no—
118C3×C22⋊Q8—232no—
119C2×C3×C4⋊C4—22no—
120C2×C3×C4⋊C4—22no—
121C2×C3×C4⋊C4—22no—
122C2×C3×C4⋊C4—22no—
123C2×C3×C4⋊C4—22no—
124C2×C3×C4⋊C4—22no—
125C2×C3×C4⋊C4—22no—
126C2×C3×C4⋊C4D414yescomplemented
127C2×C3×C4⋊C4D414yescomplemented
128C2×C3×C22⋊C4—22no—
129C2×C3×C22⋊C4—22no—
130C2×C3×C22⋊C4—22no—
131C2×C3×C22⋊C4—22no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4D414yes—
134C2×#217—22no—
135C2×#217—22no—
136C2×#217—22no—
137C2×#217—22no—
138C2×#217—22no—
139C2×#217—41no—
140C2×#217—41no—
141C2×#217—41no—
142C2×#217—41no—
143C2×(C2×D3)⋊C4—22no—
144C2×(C2×D3)⋊C4—22no—
145C2×(C2×D3)⋊C4—22no—
146C2×(C2×D3)⋊C4—22no—
147C2×(C2×D3)⋊C4—22no—
148C2×(C2×D3)⋊C4—22no—
149C2×(C2×D3)⋊C4—22no—
150C2×(C2×D3)⋊C4—22no—
151C2×(C2×D3)⋊C4—22no—
152C2×(C2×D3)⋊C4—22no—
153C2×(C2×D3)⋊C4—41no—
154C2×(C2×D3)⋊C4—41no—
155C2×(C2×D3)⋊C4—41no—
156C2×(C2×D3)⋊C4—41no—
157C2×(C2×D3)⋊C4D414yes—
158C2×C4⋊Dic3—22no—
159C2×C4⋊Dic3—41no—
160C2×C4⋊Dic3—41no—
161C2×Dic3⋊C4—22no—
162C2×Dic3⋊C4—22no—
163C2×Dic3⋊C4—41no—
164C3⋊#95—22no—
165C3⋊#95—22no—
166C3⋊#95—22no—
167C3⋊#95—22no—
168C3⋊#95—22no—
169C3⋊#95—22no—
170C3⋊#95—22no—
171C3⋊#95—22no—
172C3⋊#95—22no—
173C3⋊#95—22no—
174C3⋊#95—22no—
175C3⋊#95—41no—
176C3⋊#95—41no—
177C3⋊#95—41no—
178C3⋊#95—41no—
179C3⋊#95—41no—
180C23×Q8C2×D311yescharacteristic
181C23×D4—31no—
182C24×C4—31no—
183C24×C4C2×D311yescharacteristic
184C2×C22⋊Q8—24no—
185C2×C22⋊Q8—24no—
186C2×C22⋊Q8—24no—
187C22×C4⋊C4—31no—
188C22×C4⋊C4—31no—
189C22×C4⋊C4C2×D311yescharacteristic
190C22×C4⋊C4C2×D311yescharacteristic
191C22×C4⋊C4C2×D311yescharacteristic
192C22×C22⋊C4—31no—
193C22×C22⋊C4—31no—
194C22×C22⋊C4—31no—
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4C2×D311yescharacteristic
201C22×C22⋊C4C2×D311yescharacteristic
202#393—64no—
203#386—64no—
204#386—64no—
205#385—64no—
206#380—64no—
207C2×#95—31no—
208C2×#95—31no—
209C2×#95—31no—
210C2×#95—31no—
211C2×#95—31no—
212C2×#95—31no—
213C2×#95—31no—
214C2×#95—31no—
215C2×#95—31no—
216C2×#95—31no—
217C2×#95—31no—
218C2×#95—31no—
219C2×#95—31no—
220C2×#95—31no—
221C2×#95—31no—
222C2×#95—31no—
223C24×C3—21no—
224C24×C3—21no—
225C24×C3—21no—
226C24×C3—21no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—21no—
230C24×C3—21no—
231C24×C3—21no—
232C24×C3—21no—
233C24×C3—21no—
234C24×C3—21no—
235C24×C3C2×D412yes—
236C24×C3C2×Q812yes—
237C24×C3#4112yes—
238C24×C3C2411yescharacteristic
239C23×D3—21no—
240C23×D3—21no—
241C23×D3—21no—
242C23×D3—21no—
243C23×D3—21no—
244C23×D3—21no—
245C23×D3—21no—
246C23×D3—21no—
247C23×D3—21no—
248C23×D3—21no—
249C23×D3—21no—
250C23×D3—21no—
251C23×D3C2×D412yes—
252C23×D3C2×Q812yes—
253C23×D3#4112yes—
254C2×C3×Q8—28no—
255C2×C3×Q8—44no—
256C2×C3×Q8—44no—
257C2×C3×Q8—44no—
258C2×C3×Q8—44no—
259C2×C3×Q8—44no—
260C2×C3×Q8—44no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—21no—
264C22×C3×C4—21no—
265C22×C3×C4—21no—
266C22×C3×C4—21no—
267C22×C3×C4—21no—
268C22×C3×C4—21no—
269C22×C3×C4—28no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—21no—
274C22×C3×C4—21no—
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—44no—
295C22×C3×C4—44no—
296C22×C3×C4—44no—
297C22×C3×C4—44no—
298C22×C3×C4—44no—
299C22×C3×C4—44no—
300C22×C3×C4C2×D412yes—
301C22×C3×C4C2×D412yes—
302C22×C3×C4C2×D412yes—
303C22×C3×C4C2×D412yes—
304C22×C3×C4C2×D412yes—
305C22×C3×C4C2×D412yes—
306C22×C3×C4C2×D412yes—
307C22×C3×C4C2×D412yes—
308C22×C3×C4C2×D412yes—
309C22×C3×C4#4112yes—
310C2×#67—28no—
311C2×#67—28no—
312C2×#67—44no—
313C2×#67—44no—
314C2×#67—44no—
315C2×#67—44no—
316C2×#67—44no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3—21no—
327C22×Dic3—21no—
328C22×Dic3—21no—
329C22×Dic3—21no—
330C22×Dic3—21no—
331C22×Dic3—21no—
332C22×Dic3—21no—
333C22×Dic3—21no—
334C22×Dic3—21no—
335C22×Dic3—21no—
336C22×Dic3—21no—
337C22×Dic3—21no—
338C22×Dic3—21no—
339C22×Dic3—21no—
340C22×Dic3—21no—
341C22×Dic3—21no—
342C22×Dic3—21no—
343C22×Dic3—21no—
344C22×Dic3—21no—
345C22×Dic3—21no—
346C22×Dic3—21no—
347C22×Dic3—21no—
348C22×Dic3—21no—
349C22×Dic3—21no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C22×Dic3—21no—
353C22×Dic3—21no—
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C22×Dic3—21no—
358C22×Dic3—21no—
359C22×Dic3—21no—
360C22×Dic3—21no—
361C22×Dic3—21no—
362C22×Dic3—21no—
363C22×Dic3C2×D412yes—
364C22×Dic3C2×Q812yes—
365C22×Dic3#4112yes—
366C2×C4×D3—28no—
367C2×C4×D3—44no—
368C2×C4×D3—44no—
369C2×C4×D3—44no—
370C2×C4×D3—44no—
371C2×C4×D3—44no—
372C2×C4×D3—44no—
373C3×C4⋊C4—28no—
374C3×C4⋊C4—28no—
375C3×C4⋊C4—28no—
376C3×C22⋊C4—28no—
377C3×C22⋊C4—28no—
378#217—44no—
379#217—44no—
380#217—44no—
381(C2×D3)⋊C4—28no—
382(C2×D3)⋊C4—44no—
383(C2×D3)⋊C4—44no—
384(C2×D3)⋊C4—44no—
385(C2×D3)⋊C4—44no—
386C4⋊Dic3—44no—
387Dic3⋊C4—44no—
388C25—31no—
389C25C22×D311yescharacteristic
390C22×Q8—22no—
391C22×Q8—22no—
392C22×Q8—22no—
393C22×Q8—22no—
394C22×Q8—22no—
395C22×Q8—41no—
396C22×Q8—41no—
397C22×D4—34no—
398C22×D4—62no—
399C22×D4—62no—
400C22×D4—62no—
401C22×D4—62no—
402C22×D4—121no—
403C22×D4—121no—
404C23×C4—22no—
405C23×C4—22no—
406C23×C4—22no—
407C23×C4—22no—
408C23×C4—22no—
409C23×C4—31no—
410C23×C4—31no—
411C23×C4—31no—
412C23×C4—31no—
413C23×C4—31no—
414C23×C4—31no—
415C23×C4—31no—
416C23×C4—41no—
417C23×C4—41no—
418C23×C4—62no—
419C23×C4—62no—
420C23×C4—62no—
421C23×C4—62no—
422C23×C4—62no—
423C23×C4—121no—
424C23×C4—121no—
425C23×C4C22×D311yescharacteristic
426C23×C4C22×D311yescharacteristic
427C23×C4C22×D311yescharacteristic
428C23×C4C22×D311yescharacteristic
429C23×C4C22×D311yescharacteristic
430C23×C4C22×D311yescharacteristic
431C22⋊Q8—232no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—62no—
440C2×C4⋊C4—62no—
441C2×C4⋊C4—62no—
442C2×C4⋊C4—121no—
443C2×C4⋊C4—121no—
444C2×C4⋊C4—121no—
445C2×C4⋊C4#6714yescomplemented
446C2×C4⋊C4#6714yescomplemented
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—22no—
451C2×C22⋊C4—22no—
452C2×C22⋊C4—34no—
453C2×C22⋊C4—62no—
454C2×C22⋊C4—62no—
455C2×C22⋊C4—62no—
456C2×C22⋊C4—62no—
457C2×C22⋊C4—62no—
458C2×C22⋊C4—62no—
459C2×C22⋊C4—62no—
460C2×C22⋊C4—62no—
461C2×C22⋊C4—62no—
462C2×C22⋊C4—62no—
463C2×C22⋊C4—62no—
464C2×C22⋊C4—62no—
465C2×C22⋊C4—62no—
466C2×C22⋊C4—62no—
467C2×C22⋊C4—62no—
468C2×C22⋊C4—121no—
469C2×C22⋊C4—121no—
470C2×C22⋊C4—121no—
471C2×C22⋊C4—121no—
472C2×C22⋊C4—121no—
473C2×C22⋊C4—121no—
474C2×C22⋊C4—121no—
475C2×C22⋊C4—121no—
476C2×C22⋊C4#6714yes—
477#95—62no—
478#95—62no—
479#95—62no—
480#95—62no—
481#95—62no—
482#95—62no—
483#95—62no—
484#95—62no—
485#95—62no—
486#95—62no—
487#95—62no—
488#95—121no—
489#95—121no—
490#95—121no—
491#95—121no—
492#95—121no—
493C23×C3—22no—
494C23×C3—22no—
495C23×C3—22no—
496C23×C3—22no—
497C23×C3—22no—
498C23×C3—22no—
499C23×C3—22no—
500C23×C3—22no—
501C23×C3—22no—
502C23×C3—22no—
503C23×C3—22no—
504C23×C3—22no—
505C23×C3—22no—
506C23×C3—22no—
507C23×C3—22no—
508C23×C3—22no—
509C23×C3—22no—
510C23×C3—22no—
511C23×C3—41no—
512C23×C3—41no—
513C23×C3—41no—
514C23×C3—41no—
515C23×C3—41no—
516C23×C3—41no—
517C23×C3—41no—
518C23×C3—41no—
519C23×C3—41no—
520C23×C3—41no—
521C23×C3—41no—
522C23×C3—41no—
523C23×C3—41no—
524C23×C3—41no—
525C23×C3—41no—
526C23×C3—41no—
527C23×C3C22⋊Q814yes—
528C23×C3C22×D411yescharacteristic
529C23×C3C22×D411yescharacteristic
530C23×C3C22×D411yescharacteristic
531C23×C3C22×D411yescharacteristic
532C23×C3C22×Q811yescharacteristic
533C23×C3C2×#4111yescharacteristic
534C23×C3C2×#4111yescharacteristic
535C23×C3C2×#4111yescharacteristic
536C23×C3C2×#4111yescharacteristic
537C23×C3H(5,𝔽2)11yescharacteristic
538C23×C3H(5,𝔽2)11yescharacteristic
539C23×C3H(5,𝔽2)11yescharacteristic
540C23×C3H(5,𝔽2)11yescharacteristic
541C23×C32−1+411yescharacteristic
542C23×C32−1+411yescharacteristic
543C22×D3—22no—
544C22×D3—22no—
545C22×D3—22no—
546C22×D3—22no—
547C22×D3—22no—
548C22×D3—22no—
549C22×D3—22no—
550C22×D3—22no—
551C22×D3—22no—
552C22×D3—22no—
553C22×D3—22no—
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—22no—
557C22×D3—22no—
558C22×D3—22no—
559C22×D3—22no—
560C22×D3—22no—
561C22×D3—41no—
562C22×D3—41no—
563C22×D3—41no—
564C22×D3—41no—
565C22×D3—41no—
566C22×D3—41no—
567C22×D3—41no—
568C22×D3—41no—
569C22×D3—41no—
570C22×D3—41no—
571C22×D3—41no—
572C22×D3—41no—
573C22×D3—41no—
574C22×D3—41no—
575C22×D3—41no—
576C22×D3—41no—
577C22×D3C22⋊Q814yescomplemented
578C3×Q8—416no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—22no—
591C2×C3×C4—22no—
592C2×C3×C4—22no—
593C2×C3×C4—22no—
594C2×C3×C4—22no—
595C2×C3×C4—22no—
596C2×C3×C4—22no—
597C2×C3×C4—22no—
598C2×C3×C4—22no—
599C2×C3×C4—22no—
600C2×C3×C4—22no—
601C2×C3×C4—22no—
602C2×C3×C4—22no—
603C2×C3×C4—416no—
604C2×C3×C4—41no—
605C2×C3×C4—41no—
606C2×C3×C4—41no—
607C2×C3×C4—41no—
608C2×C3×C4—41no—
609C2×C3×C4—41no—
610C2×C3×C4—41no—
611C2×C3×C4—41no—
612C2×C3×C4—41no—
613C2×C3×C4—41no—
614C2×C3×C4—41no—
615C2×C3×C4—41no—
616C2×C3×C4—41no—
617C2×C3×C4—41no—
618C2×C3×C4—41no—
619C2×C3×C4—41no—
620C2×C3×C4#12014yes—
621C2×C3×C4#12114yes—
622#67—416no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—22no—
626C2×Dic3—22no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—22no—
630C2×Dic3—22no—
631C2×Dic3—22no—
632C2×Dic3—41no—
633C2×Dic3—41no—
634C2×Dic3—41no—
635C2×Dic3—41no—
636C2×Dic3—41no—
637C2×Dic3—41no—
638C2×Dic3—41no—
639C2×Dic3—41no—
640C2×Dic3—41no—
641C2×Dic3—41no—
642C2×Dic3—41no—
643C2×Dic3—41no—
644C2×Dic3—41no—
645C2×Dic3—41no—
646C2×Dic3—41no—
647C2×Dic3—41no—
648C2×Dic3—41no—
649C2×Dic3—41no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652C2×Dic3—41no—
653C2×Dic3—41no—
654C2×Dic3—41no—
655C2×Dic3—41no—
656C2×Dic3—41no—
657C2×Dic3—41no—
658C2×Dic3—41no—
659C2×Dic3—41no—
660C2×Dic3—41no—
661C2×Dic3—41no—
662C2×Dic3—41no—
663C2×Dic3—41no—
664C2×Dic3—41no—
665C2×Dic3—41no—
666C2×Dic3—41no—
667C2×Dic3—41no—
668C2×Dic3—41no—
669C2×Dic3—41no—
670C2×Dic3—41no—
671C2×Dic3—41no—
672C4×D3—416no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—32no—
686C24—32no—
687C24—32no—
688C24—61no—
689C24—61no—
690C24—61no—
691C24—61no—
692C24—61no—
693C24—61no—
694C24—61no—
695C24—61no—
696C24—61no—
697C24—61no—
698C24—61no—
699C24—61no—
700C24D3×Q812yes—
701C24#23912yes—
702C24C2×#6712yes—
703C24C23×D311yescharacteristic
704C2×Q8—28no—
705C2×Q8—44no—
706C2×Q8—44no—
707C2×Q8—44no—
708C2×Q8—44no—
709C2×Q8—44no—
710C2×Q8—44no—
711C2×D4—68no—
712C2×D4—68no—
713C2×D4—124no—
714C2×D4—124no—
715C2×D4—124no—
716C2×D4—124no—
717C2×D4—124no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—28no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—32no—
752C22×C4—32no—
753C22×C4—32no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—68no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4—61no—
766C22×C4—61no—
767C22×C4—61no—
768C22×C4—61no—
769C22×C4—61no—
770C22×C4—61no—
771C22×C4—61no—
772C22×C4—61no—
773C22×C4—61no—
774C22×C4—61no—
775C22×C4—61no—
776C22×C4—61no—
777C22×C4—61no—
778C22×C4—61no—
779C22×C4—61no—
780C22×C4—61no—
781C22×C4—61no—
782C22×C4—61no—
783C22×C4—61no—
784C22×C4—61no—
785C22×C4—61no—
786C22×C4—61no—
787C22×C4—61no—
788C22×C4—61no—
789C22×C4—61no—
790C22×C4—61no—
791C22×C4—61no—
792C22×C4—61no—
793C22×C4—61no—
794C22×C4—61no—
795C22×C4—61no—
796C22×C4—61no—
797C22×C4—61no—
798C22×C4—61no—
799C22×C4—61no—
800C22×C4—61no—
801C22×C4—61no—
802C22×C4—61no—
803C22×C4—61no—
804C22×C4—61no—
805C22×C4—61no—
806C22×C4—61no—
807C22×C4—124no—
808C22×C4—124no—
809C22×C4—124no—
810C22×C4—124no—
811C22×C4—124no—
812C22×C4—124no—
813C22×C4D3×D412yes—
814C22×C4#23712yes—
815C22×C4C2×#6712yes—
816C22×C4C2×#6712yes—
817C22×C4C2×#6712yes—
818C22×C4C2×#6712yes—
819C22×C4C2×#6712yes—
820C22×C4C2×#6712yes—
821C22×C4C2×#6712yes—
822C22×C4C2×#6712yes—
823C4⋊C4—28no—
824C4⋊C4—28no—
825C4⋊C4—28no—
826C4⋊C4—124no—
827C4⋊C4—124no—
828C22⋊C4—28no—
829C22⋊C4—28no—
830C22⋊C4—68no—
831C22⋊C4—124no—
832C22⋊C4—124no—
833C22⋊C4—124no—
834C22⋊C4—124no—
835C22⋊C4—124no—
836C22⋊C4—124no—
837C22⋊C4—124no—
838C22×C3—24no—
839C22×C3—24no—
840C22×C3—24no—
841C22×C3—42no—
842C22×C3—42no—
843C22×C3—42no—
844C22×C3—42no—
845C22×C3—42no—
846C22×C3—42no—
847C22×C3—42no—
848C22×C3—42no—
849C22×C3—42no—
850C22×C3—42no—
851C22×C3—42no—
852C22×C3—42no—
853C22×C3C2×#12011yescharacteristic
854C22×C3C2×#12111yescharacteristic
855C22×C3C2×C22⋊Q811yescharacteristic
856C22×C3C2×C22⋊Q811yescharacteristic
857C22×C3#52511yescharacteristic
858C22×C3#52911yescharacteristic
859C22×C3#53511yescharacteristic
860C22×C3#53511yescharacteristic
861C22×C3#53611yescharacteristic
862C22×C3#53711yescharacteristic
863C22×C3#53811yescharacteristic
864C22×C3#53911yescharacteristic
865C22×C3#54211yescharacteristic
866C22×C3#54211yescharacteristic
867C22×C3#54311yescharacteristic
868C22×C3D4211yescharacteristic
869C22×C3D4211yescharacteristic
870C22×C3#54611yescharacteristic
871C22×C3#54611yescharacteristic
872C22×C3#54611yescharacteristic
873C22×C3#54611yescharacteristic
874C22×C3#54611yescharacteristic
875C22×C3#54611yescharacteristic
876C22×C3#54611yescharacteristic
877C22×C3#54711yescharacteristic
878C22×C3#54811yescharacteristic
879C22×C3#54811yescharacteristic
880C22×C3D4×Q811yescharacteristic
881C22×C3D4×Q811yescharacteristic
882C22×C3#55111yescharacteristic
883C22×C3#55211yescharacteristic
884C22×C3#55411yescharacteristic
885C22×C3#55411yescharacteristic
886C22×C3#56211yescharacteristic
887C22×C3#56211yescharacteristic
888C2×D3—24no—
889C2×D3—24no—
890C2×D3—24no—
891C2×D3—42no—
892C2×D3—42no—
893C2×D3—42no—
894C2×D3—42no—
895C2×D3—42no—
896C2×D3—42no—
897C2×D3—42no—
898C2×D3—42no—
899C2×D3—42no—
900C2×D3—42no—
901C2×D3—42no—
902C2×D3—42no—
903C3×C4—24no—
904C3×C4—24no—
905C3×C4—42no—
906C3×C4—42no—
907C3×C4—42no—
908C3×C4—42no—
909Dic3—42no—
910Dic3—42no—
911Dic3—42no—
912Dic3—81no—
913Dic3—81no—
914Dic3—81no—
915Dic3—81no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—34no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—62no—
952C23—62no—
953C23—62no—
954C23—62no—
955C23—62no—
956C23—62no—
957C23—62no—
958C23—62no—
959C23—62no—
960C23—62no—
961C23—62no—
962C23—62no—
963C23—62no—
964C23—62no—
965C23—62no—
966C23—62no—
967C23—62no—
968C23—62no—
969C23—121no—
970C23—121no—
971C23—121no—
972C23—121no—
973C23—121no—
974C23—121no—
975C23—121no—
976C23—121no—
977C23—121no—
978C23—121no—
979C23—121no—
980C23—121no—
981C23—121no—
982C23—121no—
983C23—121no—
984C23—121no—
985C23#94614yes—
986C23C2×D3×D411yescharacteristic
987C23C2×#23711yescharacteristic
988C23#100411yescharacteristic
989C23#100411yescharacteristic
990C23C2×D3×Q811yescharacteristic
991C23C2×#23911yescharacteristic
992C23#100711yescharacteristic
993C23#100711yescharacteristic
994C23D3×#4111yescharacteristic
995C23D3×#4111yescharacteristic
996C23#100911yescharacteristic
997C23#100911yescharacteristic
998C23C22×#6711yescharacteristic
999C23C22×#6711yescharacteristic
1000C23C22×#6711yescharacteristic
1001Q8—416no—
1002D4—1216no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—416no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—62no—
1045C2×C4—62no—
1046C2×C4—62no—
1047C2×C4—62no—
1048C2×C4—62no—
1049C2×C4—62no—
1050C2×C4—62no—
1051C2×C4—62no—
1052C2×C4—62no—
1053C2×C4—1216no—
1054C2×C4—121no—
1055C2×C4—121no—
1056C2×C4—121no—
1057C2×C4—121no—
1058C2×C4—121no—
1059C2×C4—121no—
1060C2×C4—121no—
1061C2×C4—121no—
1062C2×C4—121no—
1063C2×C4—121no—
1064C2×C4—121no—
1065C2×C4—121no—
1066C2×C4—121no—
1067C2×C4—121no—
1068C2×C4—121no—
1069C2×C4—121no—
1070C2×C4—121no—
1071C2×C4—121no—
1072C2×C4—121no—
1073C2×C4—121no—
1074C2×C4—121no—
1075C2×C4—121no—
1076C2×C4—121no—
1077C2×C4—121no—
1078C2×C4—121no—
1079C2×C4—121no—
1080C2×C4—121no—
1081C2×C4—121no—
1082C2×C4—121no—
1083C2×C4—121no—
1084C2×C4—121no—
1085C2×C4—121no—
1086C2×C4—121no—
1087C2×C4—121no—
1088C2×C4—121no—
1089C2×C4—121no—
1090C2×C4—121no—
1091C2×C4—121no—
1092C2×C4—121no—
1093C2×C4—121no—
1094C2×C4#93814yes—
1095C2×C4#95314yes—
1096C2×C3—44no—
1097C2×C3#240411yescharacteristic
1098C2×C3#240811yescharacteristic
1099C2×C3#240911yescharacteristic
1100C2×C3#241711yescharacteristic
1101C2×C3#242711yescharacteristic
1102C2×C3#243711yescharacteristic
1103C2×C3#244911yescharacteristic
1104C2×C3#245011yescharacteristic
1105C2×C3#247711yescharacteristic
1106C2×C3#267211yescharacteristic
1107C2×C3#267611yescharacteristic
1108C2×C3#268711yescharacteristic
1109C2×C3#269211yescharacteristic
1110C2×C3#269211yescharacteristic
1111C2×C3#269611yescharacteristic
1112D3—44no—
1113C22—24no—
1114C22—24no—
1115C22—24no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—64no—
1129C22—64no—
1130C22—64no—
1131C22—122no—
1132C22—122no—
1133C22—122no—
1134C22—122no—
1135C22—122no—
1136C22—122no—
1137C22—122no—
1138C22—122no—
1139C22—122no—
1140C22—122no—
1141C22—122no—
1142C22—122no—
1143C22#562411yescharacteristic
1144C22D3×C22⋊Q811yescharacteristic
1145C22#562911yescharacteristic
1146C22#563011yescharacteristic
1147C22#563111yescharacteristic
1148C22#563411yescharacteristic
1149C22#563511yescharacteristic
1150C22#563611yescharacteristic
1151C22#563711yescharacteristic
1152C22#563811yescharacteristic
1153C22#563911yescharacteristic
1154C22#564011yescharacteristic
1155C22#564311yescharacteristic
1156C22#564411yescharacteristic
1157C22#564711yescharacteristic
1158C22#564711yescharacteristic
1159C22C2×#93811yescharacteristic
1160C22D4×#6711yescharacteristic
1161C22D4×#6711yescharacteristic
1162C22#580511yescharacteristic
1163C22#580611yescharacteristic
1164C22#580611yescharacteristic
1165C22C2×#94611yescharacteristic
1166C22Q8×#6711yescharacteristic
1167C22Q8×#6711yescharacteristic
1168C22#581611yescharacteristic
1169C22#581711yescharacteristic
1170C22#581711yescharacteristic
1171C22#582811yescharacteristic
1172C22#582911yescharacteristic
1173C22#582911yescharacteristic
1174C22#582911yescharacteristic
1175C22#582911yescharacteristic
1176C22#583011yescharacteristic
1177C22C2×#95311yescharacteristic
1178C4—24no—
1179C4—24no—
1180C4—42no—
1181C4—42no—
1182C4—42no—
1183C4—42no—
1184C4—122no—
1185C4—122no—
1186C4—122no—
1187C4—241no—
1188C4—241no—
1189C4—241no—
1190C4—241no—
1191C3#1532311yescharacteristic, complemented, Sylow
1192C2—44no—
1193C2—124no—
1194C2#8275211yescharacteristic
1195C2#8275611yescharacteristic
1196C2#8276511yescharacteristic
1197C2#8277011yescharacteristic
1198C2#8279411yescharacteristic
1199C2#8279711yescharacteristic
1200C2#8279811yescharacteristic
1201C2#8281611yescharacteristic
1202C2#8281711yescharacteristic
1203C2#8282611yescharacteristic
1204C2#8282711yescharacteristic
1205C2#8283011yescharacteristic
1206C2#8405311yescharacteristic
1207C2#8406811yescharacteristic
1208C2#8409611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×C22⋊Q8C2
prime radicalC23×#67C22
hypercenterC22×C22⋊Q8D3
hypocenterC3#15323
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C3×C22⋊Q8C2semidirect
2. C2×#5231C2semidirect
4. C2×#4989C2semidirect
5. C2×#4987C2semidirect
7. #72134C2semidirect
8. #72127C2semidirect
9. #71570C2semidirect
10. #71569C2semidirect
11. #71566C2semidirect
12. #71565C2semidirect
14. #71547C2semidirect
15. #71546C2semidirect
60. C22×C22⋊Q8D3semidirect
103. C22×#67Q8semidirect
126. C2×C3×C4⋊C4D4semidirect
127. C2×C3×C4⋊C4D4semidirect
445. C2×C4⋊C4#67semidirect
446. C2×C4⋊C4#67semidirect
577. C22×D3C22⋊Q8semidirect
1191. C3#15323semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×C3×C22⋊Q82
C2×#52312
C2×#52132
C2×#49892
C2×#49872
C2×#49562
#721342
#721272
#715702
#715692
#715662
#715652
#715502
#715472
#715462
#153233